In recent years, local differential privacy (LDP) has emerged as a technique of choice for privacy-preserving data collection in several scenarios when the aggregator is not trustworthy. LDP provides client-side privacy by adding noise at the user's end. Thus, clients need not rely on the trustworthiness of the aggregator. In this work, we provide a noise-aware probabilistic modeling framework, which allows Bayesian inference to take into account the noise added for privacy under LDP, conditioned on locally perturbed observations. Stronger privacy protection (compared to the central model) provided by LDP protocols comes at a much harsher privacy-utility trade-off. Our framework tackles several computational and statistical challenges posed by LDP for accurate uncertainty quantification under Bayesian settings. We demonstrate the efficacy of our framework in parameter estimation for univariate and multi-variate distributions as well as logistic and linear regression.

Aggregated predictors are obtained by making a set of basic predictors vote according to some weights, that is, to some probability distribution. Randomized predictors are obtained by sampling in a set of basic predictors, according to some prescribed probability distribution. Thus, aggregated and randomized predictors have in common that they are not defined by a minimization problem, but by a probability distribution on the set of predictors. In statistical learning theory, there is a set of tools designed to understand the generalization ability of such procedures: PAC-Bayesian or PAC-Bayes bounds. Since the original PAC-Bayes bounds of D. McAllester, these tools have been considerably improved in many directions (we will for example describe a simplified version of the localization technique of O. Catoni that was missed by the community, and later rediscovered as "mutual information bounds"). Very recently, PAC-Bayes bounds received a considerable attention: for example there was workshop on PAC-Bayes at NIPS 2017, "(Almost) 50 Shades of Bayesian Learning: PAC-Bayesian trends and insights", organized by B. Guedj, F. Bach and P. Germain. One of the reason of this recent success is the successful application of these bounds to neural networks by G. Dziugaite and D. Roy. An elementary introduction to PAC-Bayes theory is still missing. This is an attempt to provide such an introduction.

Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility especially in high dimensions, while commonly used non-parametric methods suffer from the curse of dimensionality. A popular remedy is to construct a tree-based hierarchy of conditional bivariate copulas. In this paper, we propose a flexible, yet conceptually simple alternative based on implicit generative neural networks. The key challenge is to ensure marginal uniformity of the estimated copula distribution. We achieve this by learning a multivariate latent distribution with unspecified marginals but the desired dependency structure. By applying the probability integral transform, we can then obtain samples from the high-dimensional copula distribution without relying on parametric assumptions or the need to find a suitable tree structure. Experiments on synthetic and real data from finance, physics, and image generation demonstrate the performance of this approach.

ML needs to account for uncertainty! Have you heard of probabilistic programming? It's a programming paradigm in which you can easily specify probabilistic models and perform inference on them. These languages greatly simplify the task of creating systems that handle uncertainty. For example, Pyro (from Uber AI Labs) enables flexible and expressive deep probabilistic modeling, unifying the best of modern deep learning and Bayesian modeling. And while we won't touch on probabilistic programming in this tutorial, you may want to know why probabilistic approaches are so needed in ML and why these languages are growing so quickly.

The interdependence between nodes in graphs is key to improve class predictions on nodes and utilized in approaches like Label Propagation (LP) or in Graph Neural Networks (GNN). Nonetheless, uncertainty estimation for non-independent node-level predictions is under-explored. In this work, we explore uncertainty quantification for node classification in three ways: (1) We derive three axioms explicitly characterizing the expected predictive uncertainty behavior in homophilic attributed graphs. (2) We propose a new model Graph Posterior Network (GPN) which explicitly performs Bayesian posterior updates for predictions on interdependent nodes. GPN provably obeys the proposed axioms. (3) We extensively evaluate GPN and a strong set of baselines on semi-supervised node classification including detection of anomalous features, and detection of left-out classes. GPN outperforms existing approaches for uncertainty estimation in the experiments.

Conceptual Graphs (CG) are a graph-based knowledge representation and reasoning formalism; fuzzy Conceptual Graphs (fCG) constitute an extension that enriches their expressiveness, exploiting the fuzzy set theory so as to relax their constraints at various levels. This paper proposes a comparative study of existing approaches over their respective advantages and possible limitations. The discussion revolves around three axes: (a) Critical view of each approach and comparison with previous propositions from the state of the art; (b) Presentation of the many possible interpretations of each definition to illustrate its potential and its limits; (c) Clarification of the part of CG impacted by the definition as well as the relaxed constraint.

Graph embedding techniques have been increasingly employed in real-world machine learning tasks on graph-structured data, such as social recommendations and protein structure modeling. Since the generation of a graph is inevitably affected by some sensitive node attributes (such as gender and age of users in a social network), the learned graph representations can inherit such sensitive information and introduce undesirable biases in downstream tasks. Most existing works on debiasing graph representations add ad-hoc constraints on the learned embeddings to restrict their distributions, which however compromise the utility of resulting graph representations in downstream tasks. In this paper, we propose a principled new way for obtaining unbiased representations by learning from an underlying bias-free graph that is not influenced by sensitive attributes. Based on this new perspective, we propose two complementary methods for uncovering such an underlying graph with the goal of introducing minimum impact on the utility of learned representations in downstream tasks. Both our theoretical justification and extensive experiment comparisons against state-of-the-art solutions demonstrate the effectiveness of our proposed methods.

Driving styles summarize different driving behaviors that reflect in the movements of the vehicles. These behaviors may indicate a tendency to perform riskier maneuvers, consume more fuel or energy, break traffic rules, or drive carefully. Therefore, this paper presents a driving style recognition using Interval Type-2 Fuzzy Inference System with Multiple Experts Decision-Making for classifying drivers into calm, moderate and aggressive. This system receives as input features longitudinal and lateral kinematic parameters of the vehicle motion. The type-2 fuzzy sets are more robust than type-1 fuzzy sets when handling noisy data, because their membership function are also fuzzy sets. In addition, a multiple experts approach can reduce the bias and imprecision while building the fuzzy rulebase, which stores the knowledge of the fuzzy system. The proposed approach was evaluated using descriptive statistics analysis, and compared with clustering algorithms and a type-1 fuzzy inference system. The results show the tendency to associate lower kinematic profiles for the driving styles classified with the type-2 fuzzy inference system when compared to other algorithms, which is in line with the more conservative approach adopted in the aggregation of the experts' opinions.

In human pedagogy, teachers and students can interact adaptively to maximize communication efficiency. The teacher adjusts her teaching method for different students, and the student, after getting familiar with the teacher's instruction mechanism, can infer the teacher's intention to learn faster. Recently, the benefits of integrating this cooperative pedagogy into machine concept learning in discrete spaces have been proved by multiple works. However, how cooperative pedagogy can facilitate machine parameter learning hasn't been thoroughly studied. In this paper, we propose a gradient optimization based teacher-aware learner who can incorporate teacher's cooperative intention into the likelihood function and learn provably faster compared with the naive learning algorithms used in previous machine teaching works. We give theoretical proof that the iterative teacher-aware learning (ITAL) process leads to local and global improvements. We then validate our algorithms with extensive experiments on various tasks including regression, classification, and inverse reinforcement learning using synthetic and real data. We also show the advantage of modeling teacher-awareness when agents are learning from human teachers.

This paper studies the problem of performing a sequence of optimal interventions in a causal dynamical system where both the target variable of interest and the inputs evolve over time. This problem arises in a variety of domains e.g. system biology and operational research. Dynamic Causal Bayesian Optimization (DCBO) brings together ideas from sequential decision making, causal inference and Gaussian process (GP) emulation. DCBO is useful in scenarios where all causal effects in a graph are changing over time. At every time step DCBO identifies a local optimal intervention by integrating both observational and past interventional data collected from the system. We give theoretical results detailing how one can transfer interventional information across time steps and define a dynamic causal GP model which can be used to quantify uncertainty and find optimal interventions in practice. We demonstrate how DCBO identifies optimal interventions faster than competing approaches in multiple settings and applications.